In a medium microwaveable bowl, combine the caramel bits (or squares if using), the heavy whipping cream, and the butter. Microwave for about 90 seconds, stopping to stir the mixture every 30 seconds. The first two times you stir the mixture, it will be kind of hard to stir, but you just want the mixture to move around some so it doesn't burn. Mixture will be smooth, glossy and melted around the 90 second mark. Stir in the vanilla, and then pour in the peanuts and let set for 5-10 minutes to thicken.
Line a large baking sheet with parchment paper. Drop heaping Tablespoonful mounds of the caramel peanut mixture scattered about on the baking sheet, keeping them somewhat spaced out so they don't all seep together. Once the little caramel nut puddles are made, freeze the baking sheet until the caramel mounds are solid, about 5-10 minutes. They should easily peel away from the parchment when solid enough to handle.
Prepare the vanilla CandiQuik according to package directions or until smooth and melted. Dunk each caramel nut mound into the white candy coating, using a fork to coat all sides. Return the coated polar bear paw to the baking sheet and repeat with remaining paws. Wait until chocolate hardens (should be quick on contact with the cold mixture) before serving.